Trim excess fat from the pork shoulder and cut into large chunks.
Season the pork chunks evenly with sea salt, black pepper, ground cumin, and dried oregano.
Place the seasoned pork in a slow cooker and add the minced garlic, orange juice, and 1 tablespoon of lime juice.
Cover and cook on low for 7-8 hours or on high for 4 hours until the meat is tender enough to shred easily with a fork.
Remove the pork from the slow cooker, shred with two forks, and spread the meat onto a baking sheet.
Broil the shredded pork in the oven for 3-5 minutes until the edges become golden and crispy.
While the pork broils, whisk together the Greek yogurt and 1 teaspoon of lime juice in a small bowl to create the crema.
Warm the corn tortillas in a dry skillet over medium heat until they are soft and slightly charred.
Assemble the tacos by dividing the crispy carnitas between the two tortillas.
Garnish with diced red onion, fresh cilantro, and a drizzle of the lime-yogurt crema before serving.